An efficient curved-wire integral equation solution technique

Computation of the currents on curved-wires by integral equation methods is often inefficient when the structure is tortuous but the length of wire is not large relative to the wavelength at the frequency of operation. The number of terms needed in an accurate piecewise straight model of a highly curved-wire can be large, yet, if the total length of wire is small relative to the wavelength, the current can be accurately represented by a simple linear function. A new solution method for the cured-wire integral equation is introduced. It is amenable to uncoupling of the number of segments required to accurately model the wire structure from the number of basis functions needed to represent the current. This feature lends itself to high efficiency. The principles set forth can be used to improve the efficiency of most solution techniques applied to the curved-wire integral equation. New composite basis and testing functions are defined and constructed as linear combinations of other commonly used basis and testing functions. We show how the composite basis and testing functions can lead to a reduced-rank matrix, which can be computed via a transformation of a system matrix created from traditional basis and testing functions. Supporting data demonstrate the accuracy of the technique and its effectiveness in decreasing matrix rank and solution time for curved-wire structures.